Analysis, Geometry, and Dynamical Systems Seminar

KPZ universality for last passage percolation models.

In this seminar we consider last passage percolation on $\mathbb{Z}^2$, a model in the Kardar–Parisi–Zhang (KPZ) universality class. We will investigate the universality of the limit distributions of the last passage time for different settings. In the first part we analyze the correlations of two last passage times for different ending points in a neighbourhood of the characteristic. For a general class of random initial conditions, we prove the universality of the first order correction when the two observation times are close. In the second part we consider a model of last passage percolation in half-space and we obtain the distribution of the last passage time for the stationary initial condition.